In Ptolemaic cosmology, a small circle representing a temporary adjustment to the position of a planet as it orbits the Earth. The five known planets, along with the Sun and Moon, were conceived as moving through the sky in large circular paths with the Earth at their center. As a planet moved along its path, it occasionally departed from its regular motion to follow a much smaller circle centered on the orbital path itself. These smaller circles, or epicycles, were necessary to reconcile the observed motions of the planets with a geocentric model of the universe. The epicycles of the inferior planets Mercury and Venus were fixed to the orbit of the Sun and explained why those planets were never observed far from it in the sky. The epicycles of the superior planets Mars, Jupiter, and Saturn explained why those bodies were sometimes observed to move backward in their orbits, a phenomenon known as retrograde motion and explained in a heliocentric model by the differing orbital velocities of the Earth and the planet being observed. See illustration at Ptolemaic system.

A circle whose circumference rolls along the circumference of a fixed circle, thereby generating an epicycloid or a hypocycloid.